Graph spectra are an important class of structural features on graphs that have shown promising results in enhancing Graph Neural Networks (GNNs). Despite their widespread practical use, the theoretical understanding of the power of spectral invariants -- particularly their contribution to GNNs -- remains incomplete. In this paper, we address this fundamental question through the lens of homomorphism expressivity, providing a comprehensive and quantitative analysis of the expressive power of spectral invariants. Specifically, we prove that spectral invariant GNNs can homomorphism-count exactly a class of specific tree-like graphs which we refer to as parallel trees. We highlight the significance of this result in various contexts, including establishing a quantitative expressiveness hierarchy across different architectural variants, offering insights into the impact of GNN depth, and understanding the subgraph counting capabilities of spectral invariant GNNs. In particular, our results significantly extend Arvind et al. (2024) and settle their open questions. Finally, we generalize our analysis to higher-order GNNs and answer an open question raised by Zhang et al. (2024).

Solving complex tasks in a single attempt is challenging for large language models (LLMs). Iterative interaction with the environment and feedback is often required to achieve success, making effective feedback utilization a critical topic. Existing approaches either struggle with length generalization or rely on naive retries without leveraging prior information. In this paper, we introduce FTTT, a novel paradigm that formulates feedback utilization as an optimization problem at test time. Additionally, we propose a learnable test-time optimizer, OpTune, to effectively exploit feedback. Experiments on two LLMs across four reasoning datasets demonstrate that FTTT and OpTune achieve superior scalability and performance.

Diffusion language models have emerged as a promising approach for text generation. One would naturally expect this method to be an efficient replacement for autoregressive models since multiple tokens can be sampled in parallel during each diffusion step. However, its efficiency-accuracy trade-off is not yet well understood. In this paper, we present a rigorous theoretical analysis of a widely used type of diffusion language model, the Masked Diffusion Model (MDM), and find that its effectiveness heavily depends on the target evaluation metric. Under mild conditions, we prove that when using perplexity as the metric, MDMs can achieve near-optimal perplexity in sampling steps regardless of sequence length, demonstrating that efficiency can be achieved without sacrificing performance. However, when using the sequence error rate--which is important for understanding the "correctness" of a sequence, such as a reasoning chain--we show that the required sampling steps must scale linearly with sequence length to obtain "correct" sequences, thereby eliminating MDM's efficiency advantage over autoregressive models. Our analysis establishes the first theoretical foundation for understanding the benefits and limitations of MDMs. All theoretical findings are supported by empirical studies.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet generating reliable reasoning processes remains a significant challenge. We present a unified probabilistic framework that formalizes LLM reasoning through a novel graphical model incorporating latent thinking processes and evaluation signals. Within this framework, we introduce the Bootstrapping Reinforced Thinking Process (BRiTE) algorithm, which works in two steps. First, it generates high-quality rationales by approximating the optimal thinking process through reinforcement learning, using a novel reward shaping mechanism. Second, it enhances the base LLM by maximizing the joint probability of rationale generation with respect to the model's parameters. Theoretically, we demonstrate BRiTE's convergence at a rate of $1/T$ with $T$ representing the number of iterations. Empirical evaluations on math and coding benchmarks demonstrate that our approach consistently improves performance across different base models without requiring human-annotated thinking processes. In addition, BRiTE demonstrates superior performance compared to existing algorithms that bootstrap thinking processes use alternative methods such as rejection sampling, and can even match or exceed the results achieved through supervised fine-tuning with human-annotated data.

Scaling up the vocabulary of semantic segmentation models is extremely challenging because annotating large-scale mask labels is labour-intensive and time-consuming. Recently, language-guided segmentation models have been proposed to address this challenge. However, their performance drops significantly when applied to out-of-distribution categories. In this paper, we propose a new large vocabulary semantic segmentation framework, called LarvSeg. Different from previous works, LarvSeg leverages image classification data to scale the vocabulary of semantic segmentation models as large-vocabulary classification datasets usually contain balanced categories and are much easier to obtain. However, for classification tasks, the category is image-level, while for segmentation we need to predict the label at pixel level. To address this issue, we first propose a general baseline framework to incorporate image-level supervision into the training process of a pixel-level segmentation model, making the trained network perform semantic segmentation on newly introduced categories in the classification data. We then observe that a model trained on segmentation data can group pixel features of categories beyond the training vocabulary. Inspired by this finding, we design a category-wise attentive classifier to apply supervision to the precise regions of corresponding categories to improve the model performance. Extensive experiments demonstrate that LarvSeg significantly improves the large vocabulary semantic segmentation performance, especially in the categories without mask labels. For the first time, we provide a 21K-category semantic segmentation model with the help of ImageNet21K. The code is available at https://github.com/HaojunYu1998/large_voc_seg.

Foundational models have emerged as powerful tools for addressing various tasks in clinical settings. However, their potential development to breast ultrasound analysis remains untapped. In this paper, we present BUSGen, the first foundational generative model specifically designed for breast ultrasound image analysis. Pretrained on over 3.5 million breast ultrasound images, BUSGen has acquired extensive knowledge of breast structures, pathological features, and clinical variations. With few-shot adaptation, BUSGen can generate repositories of realistic and informative task-specific data, facilitating the development of models for a wide range of downstream tasks. Extensive experiments highlight BUSGen's exceptional adaptability, significantly exceeding real-data-trained foundational models in breast cancer screening, diagnosis, and prognosis. In breast cancer early diagnosis, our approach outperformed all board-certified radiologists (n=9), achieving an average sensitivity improvement of 16.5% (P-value<0.0001). Additionally, we characterized the scaling effect of using generated data which was as effective as the collected real-world data for training diagnostic models. Moreover, extensive experiments demonstrated that our approach improved the generalization ability of downstream models. Importantly, BUSGen protected patient privacy by enabling fully de-identified data sharing, making progress forward in secure medical data utilization. An online demo of BUSGen is available at https://aibus.bio.

Diagnosis prediction is a critical task in healthcare, where timely and accurate identification of medical conditions can significantly impact patient outcomes. Traditional machine learning and deep learning models have achieved notable success in this domain but often lack interpretability which is a crucial requirement in clinical settings. In this study, we explore the use of neuro-symbolic methods, specifically Logical Neural Networks (LNNs), to develop explainable models for diagnosis prediction. Essentially, we design and implement LNN-based models that integrate domain-specific knowledge through logical rules with learnable thresholds. Our models, particularly $M_{\text{multi-pathway}}$ and $M_{\text{comprehensive}}$, demonstrate superior performance over traditional models such as Logistic Regression, SVM, and Random Forest, achieving higher accuracy (up to 80.52\%) and AUROC scores (up to 0.8457) in the case study of diabetes prediction. The learned weights and thresholds within the LNN models provide direct insights into feature contributions, enhancing interpretability without compromising predictive power. These findings highlight the potential of neuro-symbolic approaches in bridging the gap between accuracy and explainability in healthcare AI applications. By offering transparent and adaptable diagnostic models, our work contributes to the advancement of precision medicine and supports the development of equitable healthcare solutions. Future research will focus on extending these methods to larger and more diverse datasets to further validate their applicability across different medical conditions and populations.

Recent advances in large language models (LLMs) have shown significant promise, yet their evaluation raises concerns, particularly regarding data contamination due to the lack of access to proprietary training data. To address this issue, we present C$^2$LEVA, a comprehensive bilingual benchmark featuring systematic contamination prevention. C$^2$LEVA firstly offers a holistic evaluation encompassing 22 tasks, each targeting a specific application or ability of LLMs, and secondly a trustworthy assessment due to our contamination-free tasks, ensured by a systematic contamination prevention strategy that fully automates test data renewal and enforces data protection during benchmark data release. Our large-scale evaluation of 15 open-source and proprietary models demonstrates the effectiveness of C$^2$LEVA.

Large language models (LLMs) have enabled the creation of multi-modal LLMs that exhibit strong comprehension of visual data such as images and videos. However, these models usually rely on extensive visual tokens from visual encoders, leading to high computational demands, which limits their applicability in resource-constrained environments and for long-context tasks. In this work, we propose a training-free adaptive inference method for multi-modal LLMs that can accommodate a broad range of efficiency requirements with a minimum performance drop. Our method consists of a) iterative token merging based on embedding similarity before LLMs, and b) progressive token pruning within LLM layers based on multi-modal importance. With a minimalist design, our method can be applied to both video and image LLMs. Extensive experiments on diverse video and image benchmarks demonstrate that, our method substantially reduces computation load (e.g., a $\textbf{7-fold}$ reduction in FLOPs) while preserving the performance of video and image LLMs. Further, under a similar computational cost, our method outperforms the state-of-the-art methods in long video understanding (e.g., $\textbf{+4.6}$ on MLVU). Additionally, our in-depth analysis provides insights into token redundancy and LLM layer behaviors, offering guidance for future research in designing efficient multi-modal LLMs. Our code will be available at https://github.com/LaVi-Lab/AIM.

The rapid advancement of Multimodal Large Language Models (MLLMs) has significantly impacted various multimodal tasks. However, these models face challenges in tasks that require spatial understanding within 3D environments. Efforts to enhance MLLMs, such as incorporating point cloud features, have been made, yet a considerable gap remains between the models' learned representations and the inherent complexity of 3D scenes. This discrepancy largely stems from the training of MLLMs on predominantly 2D data, which restricts their effectiveness in comprehending 3D spaces. To address this issue, in this paper, we propose a novel generalist model, i.e., Video-3D LLM, for 3D scene understanding. By treating 3D scenes as dynamic videos and incorporating 3D position encoding into these representations, our Video-3D LLM aligns video representations with real-world spatial contexts more accurately. Additionally, we have implemented a maximum coverage sampling technique to optimize the balance between computational costs and performance efficiency. Extensive experiments demonstrate that our model achieves state-of-the-art performance on several 3D scene understanding benchmarks, including ScanRefer, Multi3DRefer, Scan2Cap, ScanQA, and SQA3D.